Minimization of functionals with a weak norm on solutions of the degenerate linear equation

In the work existence and uniqueness theorems are proved for a class of problems with rigid mixed control of linear distributed systems, not solvable with respect to the time derivative, with weak cost functional with respect to the state function. Abstract results are illustrated by example of the control problem for Sobolev type equation with polynomials of high order elliptic selfadjoint operators.